Approximate Solutions of Nonlinear Boundary Value Problems by Collocation Methods Compared to Newer Methods

Birkan Durak; Hasan Ömür Özer; Aziz Sezgin; Lütfi Emir Sakman

Makale detayları

Approximate Solutions of Nonlinear Boundary Value Problems by Collocation Methods Compared to Newer Methods

Yazarlar:

Birkan Durak | Hasan Ömür Özer | Aziz Sezgin | Lütfi Emir Sakman

Yayıncı:

Sakarya University

Ana Başlıklar:

Mechanical Engineering (Other)

Dergi:

Sakarya University Journal of Science Vol.27 Issue 6, pp.1345-1354

Belge Tipi:

Makale

Yayın Tarihi:

12/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001304061

pISSN:

2147-835X

Anahtar kelimeler:

Özet:

 A large variety of new methods are being developed for fast and efficient solutions of nonlinear boundary value problems. Some of these methods are, Adomian decomposition ADM, differential transform DTM, least squares vector machines LSSVMM, and multiple variational iteration MVIM. A natural question arises as to how efficient and simple to use these newer methods are compared to classical methods. One of the simplest and widely applicable classical methods is the collocation method. The overall performance of collocation method and the newer methods are compared on a number of problems, which were previously used to benchmark the newer methods. It is concluded that, at least for the problems considered, the collocation method performs as successfully as the newer methods.

 A large variety of new methods are being developed for fast and efficient solutions of nonlinear boundary value problems. Some of these methods are, Adomian decomposition ADM, differential transform DTM, least squares vector machines LSSVMM, and multiple variational iteration MVIM. A natural question arises as to how efficient and simple to use these newer methods are compared to classical methods. One of the simplest and widely applicable classical methods is the collocation method. The overall performance of collocation method and the newer methods are compared on a number of problems, which were previously used to benchmark the newer methods. It is concluded that, at least for the problems considered, the collocation method performs as successfully as the newer methods.

 A large variety of new methods are being developed for fast and efficient solutions of nonlinear boundary value problems. Some of these methods are, Adomian decomposition ADM, differential transform DTM, least squares vector machines LSSVMM, and multiple variational iteration MVIM. A natural question arises as to how efficient and simple to use these newer methods are compared to classical methods. One of the simplest and widely applicable classical methods is the collocation method. The overall performance of collocation method and the newer methods are compared on a number of problems, which were previously used to benchmark the newer methods. It is concluded that, at least for the problems considered, the collocation method performs as successfully as the newer methods.

 A large variety of new methods are being developed for fast and efficient solutions of nonlinear boundary value problems. Some of these methods are, Adomian decomposition ADM, differential transform DTM, least squares vector machines LSSVMM, and multiple variational iteration MVIM. A natural question arises as to how efficient and simple to use these newer methods are compared to classical methods. One of the simplest and widely applicable classical methods is the collocation method. The overall performance of collocation method and the newer methods are compared on a number of problems, which were previously used to benchmark the newer methods. It is concluded that, at least for the problems considered, the collocation method performs as successfully as the newer methods.

Makale detayları

Approximate Solutions of Nonlinear Boundary Value Problems by Collocation Methods Compared to Newer Methods

Yazarlar:

Birkan Durak | Hasan Ömür Özer | Aziz Sezgin | Lütfi Emir Sakman

Yayıncı:

Sakarya University

Ana Başlıklar:

Mechanical Engineering (Other)

Dergi:

Sakarya University Journal of Science Vol.27 Issue 6, pp.1345-1354

Belge Tipi:

Makale

Yayın Tarihi:

12/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001304061

pISSN:

2147-835X

Collocation method

nonlinear differential equations

boundary value problems

approximate solution.

Sayı

Makale detayları

Approximate Solutions of Nonlinear Boundary Value Problems by Collocation Methods Compared to Newer Methods

Yazarlar: Birkan Durak | Hasan Ömür Özer | Aziz Sezgin | Lütfi Emir Sakman

Yayıncı: Sakarya University

Ana Başlıklar: Mechanical Engineering (Other)

Dergi: Sakarya University Journal of Science Vol.27 Issue 6, pp.1345-1354

Belge Tipi: Makale

Yayın Tarihi: 12/2023

Belge Dili: İngilizce

Document ID (Org No.): 2001304061

pISSN: 2147-835X

Collocation method

nonlinear differential equations

boundary value problems

approximate solution.

Sayı

Yazarlar:

Birkan Durak | Hasan Ömür Özer | Aziz Sezgin | Lütfi Emir Sakman

Yayıncı:

Sakarya University

Ana Başlıklar:

Mechanical Engineering (Other)

Dergi:

Sakarya University Journal of Science Vol.27 Issue 6, pp.1345-1354

Belge Tipi:

Makale

Yayın Tarihi:

12/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001304061

pISSN:

2147-835X